Faculty of Chemistry and Chemical Technology, University of Ljubljana, Askerceva 5, 1000 Ljubljana, Slovenia.
J Chem Phys. 2009 Nov 21;131(19):194504. doi: 10.1063/1.3259970.
The two-dimensional Mercedes-Benz (MB) model of water has been widely studied, both by Monte Carlo simulations and by integral equation methods. Here, we study the three-dimensional (3D) MB model. We treat water as spheres that interact through Lennard-Jones potentials and through a tetrahedral Gaussian hydrogen bonding function. As the "right answer," we perform isothermal-isobaric Monte Carlo simulations on the 3D MB model for different pressures and temperatures. The purpose of this work is to develop and test Wertheim's Ornstein-Zernike integral equation and thermodynamic perturbation theories. The two analytical approaches are orders of magnitude more efficient than the Monte Carlo simulations. The ultimate goal is to find statistical mechanical theories that can efficiently predict the properties of orientationally complex molecules, such as water. Also, here, the 3D MB model simply serves as a useful workbench for testing such analytical approaches. For hot water, the analytical theories give accurate agreement with the computer simulations. For cold water, the agreement is not as good. Nevertheless, these approaches are qualitatively consistent with energies, volumes, heat capacities, compressibilities, and thermal expansion coefficients versus temperature and pressure. Such analytical approaches offer a promising route to a better understanding of water and also the aqueous solvation.
二维的奔驰（MB）水分子模型已经被广泛研究过了，其中包括蒙卡罗模拟和积分方程方法。在这里，我们研究三维（3D）MB 模型。我们将水分子视为球体，通过 Lennard-Jones 势能和四面体高斯氢键函数进行相互作用。作为“正确答案”，我们在不同的压力和温度下对 3D MB 模型进行等温等压蒙卡罗模拟。这项工作的目的是开发和测试 Wertheim 的 Ornstein-Zernike 积分方程和热力学摄动理论。这两种分析方法的效率比蒙卡罗模拟高几个数量级。最终目标是找到能够有效地预测具有复杂取向的分子（如水分子）性质的统计力学理论。此外，在这里，3D MB 模型只是作为测试这些分析方法的有用工作台。对于热水，分析理论与计算机模拟结果非常吻合。对于冷水，结果就不太理想。然而，这些方法在能量、体积、热容、压缩率和热膨胀系数与温度和压力的关系上是定性一致的。这些分析方法为更好地理解水以及水溶剂化提供了一个很有前途的途径。
